If in a moderately asymmetrical distribution the mode and the mean of the data are `6 lamda " and" 9 lamda`, respectively, then the median is

Options

A. `8 lamda`
B. `7 lamda`
C. `6 lamda`
D. `5 lamda`

Explanation

To find the median of the given moderately asymmetrical distribution where the mode is \(6\lambda\) and the mean is \(9\lambda\), we can use the relationship between mode, median, and mean for such distributions.

### Step-by-Step Solution:

1. **Identify the given values:**
- Mode (\(Mo\)) = \(6\lambda\)
- Mean (\(M\)) = \(9\lambda\)

2. **Use the formula relating mode, median, and mean:**
For a moderately asymmetrical distribution, the relationship is given by:
\[ Mo = 3 \times \text{Median} - 2 \times M \]
Substituting the known values into the formula:
\[ 6\lambda = 3 \times \text{Median} - 2 \times (9\lambda) \]

3. **Simplify the equation:**
\[ 6\lambda = 3 \times \text{Median} - 18\lambda \]
Rearranging gives:
\[ 3 \times \text{Median} = 6\lambda + 18\lambda \]
\[ 3 \times \text{Median} = 24\lambda \]

4. **Solve for the median:**
\[ \text{Median} = \frac{24\lambda}{3} \]
\[ \text{Median} = 8\lambda \]

Thus, the median of the distribution is \(8\lambda\).

### Final Answer:
The median is \(8\lambda\).